Sankalana-Vyavakalanabhyam
By addition and by subtraction (san · ka · la · na vya · va · ka · la · na · bhyam)
What it means
Solve a pair of equations by adding them together to wipe out one variable, and subtracting them to wipe out the other. No substitution needed.
Worked example
Solve x + 3y = 10 and 3x + y = 6. Add: 4x + 4y = 16, so x + y = 4. Subtract: 2x − 2y = −4, so x − y = −2. From x + y = 4 and x − y = −2: x = 1, y = 3.